If $r$ represents the radius of the orbit of the satellite of mass $m$ moving around a planet of mass $M$ , the velocity $v$ of the satellite is related as :

v^{2} = (G M / r)

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v^{2} = (G M m / r)

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v = (G M / r)

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v^{2} = (G m / r)

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Solution

The correct option is B $v^{2} = (G M / r)$
Given $, M$ is mass of planet $, m$ is mass of satellite $, r$ is radius of orbit.

Let $, v$ be velocity of the satellite

Now, for the satellite to revolve in the orbit the centripetal force must be balanced by gravitational force i.e.,

$F_{c} = F_{g} \to (1)$

we know that,

$F_{c} = \frac{m v^{2}}{r}$ and $F_{g} = G M m r^{2}$ .

Substituting these values in $(1),$

$\frac{m v^{2}}{r} = \frac{G M m}{r^{2}}$ .

After solving this equation we get
$v^{2} = \frac{G M}{r}$

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